Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #508×D71 | C2 | semidirect |
| 2. #22590659 | C2 | semidirect |
| 3. #22590656 | C2 | semidirect |
| 4. #22590654 | C2 | semidirect |
| 5. #22590651 | C2 | semidirect |
| 6. #22590649 | C2 | semidirect |
| 7. #22590647 | C2 | semidirect |
| 8. C2×#17985832 | C2 | semidirect |
| 9. C71×#2262 | C2 | semidirect |
| 12. #17986431 | C22 | semidirect |
| 16. Q32×D71 | C22 | semidirect |
| 18. D16×D71 | C22 | semidirect |
| 20. Dic1136 | C22 | semidirect |
| 21. #17985839 | C22 | semidirect |
| 22. #17985838 | C22 | semidirect |
| 23. #17985837 | C22 | semidirect |
| 24. #17985836 | C22 | semidirect |
| 25. D2272 | C22 | semidirect |
| 26. #17985834 | C22 | semidirect |
| 27. #17985832 | C22 | semidirect |
| 28. #17985832 | C22 | semidirect |
| 29. C2×C71⋊C32 | C22 | semidirect |
| 30. #508×C71 | C22 | semidirect |
| 31. Q64×C71 | C22 | semidirect |
| 32. SD64×C71 | C22 | semidirect |
| 33. D32×C71 | C22 | semidirect |
| 34. C2×C32×C71 | C22 | semidirect |
| 139. #2262 | D71 | semidirect |
| 141. C71 | #33981 | semidirect |
| 148. #508 | C2×D71 | semidirect |
| 155. Q64 | C2×D71 | semidirect |
| 159. SD64 | C2×D71 | semidirect |
| 162. D32 | C2×D71 | semidirect |
| 166. C2×C32 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D71 | 2 |
| #22590659 | 2 |
| #22590656 | 2 |
| #22590654 | 2 |
| #22590651 | 2 |
| #22590649 | 2 |
| #22590647 | 2 |
| C2×#17985832 | 2 |
| C71×#2262 | 2 |
| #33981 | 71 |